• Class Number 3440
• Term Code 3130
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Prof Lilia Ferrario
• LECTURER
• Galina Levitina
• Prof Lilia Ferrario
• Zhisong Qu
• Class Dates
• Class Start Date 22/02/2021
• Class End Date 28/05/2021
• Census Date 31/03/2021
• Last Date to Enrol 01/03/2021
SELT Survey Results

Ordinary Differential Equations and Advanced Vector Calculus (MATH6405)

This course provides an in depth exposition of the theory of differential equations and vector calculus. Applications will be related to problems mainly from the Physical Sciences.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of differential equations and vector calculus and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.
4. Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.
5. Explain the use and applications of differential equations and/or vector calculus to some topic related to undergraduate study, employment or other experience.

UG Version

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of differential equations and vector calculus and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.
4. Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.

## Research-Led Teaching

Techniques covered in this course will be linked to applications in the physical and biological sciences, engineering and information technologies, economics and commerce.

## Examination Material or equipment

A double sided A4 summary page (handwritten) is allowed in each of the exams.

## Required Resources

Students need a computer to complete the online quizzes via the WebAssign platform, and to access Wattle (they can use either an ANU computer or they can use their own device). They also need to have a webcamera if they need/choose to participate in online workshops.

Highly recommended textbooks:

"Essential Calculus" by James Stewart (2nd Edition). This is the same textbook used in MATH1013 and MATH1014.

"A First Course in Differential Equation with Modelling Applications" by Dennis G. Zill,.

Recommended student system requirements

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

## Staff Feedback

Students will be given feedback in the following forms in this course:

• feedback to whole class, groups, individuals, focus group etc

## Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

## Other Information

Please note, that where there are multiple assessment tasks of the same type, e.g weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site.

Course delivery and assessment in 2021 was adjusted due to the COVID-19 pandemic.

Teaching Activities

Lectures will be online, recorded and posted on Echo360.

Workshops and computer labs: there will be two modes of workshops. For students, who are in Canberra, there will be on-campus workshops in the location as per timetable. For the students, who are not in Canberra, the workshops will be online and be done via Zoom at the scheduled times. The number of on-campus and online workshops will be decided by week 2 and will be dependent on how many students choose on-campus workshops.

Computer Labs

Introductory Matlab sessions will be held in the second and third weeks. Students may drop in these sessions at any time they find suitable and as many times as they wish. No booking or enrolment is necessary. The purpose of these sessions is to introduce Matlab to students that haven't used it before, or are not confident in their ability to use Matlab. Demonstrators will answer your questions on Matlab. The assessments will have Matlab questions and you will need to submit Matlab code in assignments. We highly recommend to attend the introductory sessions and ask as many questions as you can. This is not a programming course and you will not be asked to do any serious Matlab programming. Rather, the idea is to use Matlab to explore the properties of different mathematical models.

Course communication

Office hours are listed on the course home page. If you would like to talk to the lecturer outside of those hours send us an e-mail (contact details are also on the home page).

If you have a question that may be of interest to the class as a whole please use the discussion board. And if you post a question on the discussion that you would like one of the lecturers to answer, please address it to us specifically so we know that you are expecting us to answer it. We will not generally get involved in the discussion, so if you do not address it to us we will assume that you are expecting another student to reply.

Please check the records in the gradebook regularly and notify your demonstrator immediately if you believe there is a mistake. The grade for each workshop and assignment will be displayed in the gradebook for three weeks, after which time we will assume the grade is correct and it will be removed from display. A running total of your grades will remain. Our reason for doing this is to encourage you to notify the demonstrators promptly if there is a mistake, while the information is still fresh in everyone's minds. It is no good coming to the lecturers at the end of the semester complaining that the grade for workshop 1 is wrong, nobody is going to remember what happened ten weeks earlier.

## Class Schedule

Week/Session Summary of Activities Assessment
1 Vector fields, Line integrals, the fundamental theorem of line integrals. Assignment 1, Test 1 Online WebAssign quiz 1
2 Green's Theorem, curl and divergence, Parametric surfaces and their areas. Assignment 1, Test 1 Online WebAssign quiz 2
3 Surface integrals, Stokes' Theorem; Research project: ODE initial value problem. Assignment 1, Test 1, Online WebAssign quiz 3
4 The Divergence Theorem, basics of ODES, separable equations; Research project: Hamiltonian systems, periodic motion. Assignment 1, Test 2 Online WebAssign quiz 4
5 First order linear ODEs, exact equations, introduction to higher order equations; Research project: Numerical time integrators, RK4, symplectic integrators. Assignment 2, Test 2 Online WebAssign quiz 5
6 Second order ODEs, method of reduction of order, second order ODEs with constant coefficients; Research project: Integrability, examples of regular and chaotic orbits. Assignment 2, Test 2 Online WebAssign quiz 6
7 Nonhomogeneous equations and their solutions; Research project: Poincare section, the standard map. Assignment 2, Test 3 Online WebAssign quiz 7
8 Higher order linear differential equations; Research project: Fixed points, linear expansion around fixed points, elliptic and hyperbolic points, islands and chaos. Assignment 3, Test 3 Online WebAssign quiz 8
9 Power series solutions; Research project: KAM theorem. Assignment 3, Test 3 Online WebAssign quiz 9
10 Special functions; Research project: Transition to global chaos, criteria to determine transition threshold. Assignment 3, Test 4 Online WebAssign quiz 10
11 Linear system of differential equations; Research project: Chaos, Liapunov exponents. Assignment 3, Test 4 Online WebAssign quiz 11
12 Phase plane for linear system, nonlinear system of differential equations, numerical solutions of ODEs; Research project: Revision and summary, presentation of research project Review Exercises

## Tutorial Registration

Workshops

Workshops will be held during the semester and will start in week 3. Please use the sign-up sheet on the front page to enrol in a workshop group (open at the end of week 1).

This is a large class, so to help distribute the resources more fairly and evenly we ask you to attend the workshop group you have been assigned to. If you do not attend the correct workshop group you will not receive a participation grade. Also, find out your demonstrator's name etc. so you can put the right information on the assignment cover sheet. If you are unable to attend a workshop due to unforeseen circumstances (e.g. illness) contact the lecturer to arrange to attend another workshop.

To participate in online workshop students need to have their camera turned on for the duration of the workshop. The exemptions can be obtained from the lecturers.

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Mid-semester exam 20 % 29/03/2021 23/04/2021 1,2,3,4,5
End of semester exam 33 % 03/06/2021 01/07/2021 1,2,3,4,5
Workshop participation 4 % 22/02/2021 28/05/2021 1,2,3,4,5
Assignments 6 % * * 1,2,3,4,5
Online tests 11 % * * 1,2,3,4,5
Quizzes 6 % 01/03/2021 28/05/2021 1,2,3,4,5
Research project 20 % 02/06/2020 16/06/2020 1,2,3,4,5

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

## Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

## Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

## Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

## Participation

Workshop participation: At the start of each workshop, the class will divide into small groups so that each person presenting a solution can check their answer with their peers and demonstrator. The person presenting the solution should feel free to ask for as much help as they want. All students should participate and ask questions. The remaining time will be left free for students to ask questions or get some feedback about the assignments etc. If students do not attend the correct workshop group they will not receive a participation grade. However, If students are unable to attend a workshop due to unforeseen circumstances (e.g. illness) they must contact the lecturer to arrange to attend another workshop. Demonstrators will keep track of students' participation. This means that students are encouraged to ask questions and contribute to the running of the workshops. It is not enough for students to turn up. They need to actively participate and work together.

## Examination(s)

Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Value: 20 %
Due Date: 29/03/2021
Return of Assessment: 23/04/2021
Learning Outcomes: 1,2,3,4,5

Mid-semester exam

The date range is an general indication of when the mid-semester exam will be held. Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and location of the mid semester exam. The mid-semester exam will be in Wattle and invigilated using Proctorio.

Value: 33 %
Due Date: 03/06/2021
Return of Assessment: 01/07/2021
Learning Outcomes: 1,2,3,4,5

End of semester exam

The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location exam. The final exam will be in Wattle and invigilated using Proctorio.

• If your overall grade is a passing grade, but you get less than 45% in the final exam, you must sit further examination. If you get 45% or more in the additional exam, you will be awarded 50PS. If you get less than 45% in the additional exam, you will receive NCN.
• If your overall grade is greater than or equal to 45%, but less than 50%, you will be offered a supplementary exam. If you pass the supplementary exam you will be awarded a grade of 50PS, otherwise you will receive N.
• No further examination will be offered if your overall grade is less than 45%.

Value: 4 %
Due Date: 22/02/2021
Return of Assessment: 28/05/2021
Learning Outcomes: 1,2,3,4,5

Workshop participation

Students are expected to contribute on an on-going basis throughout the semester. The date range for this task comprises the start of the semester and the last day of the teaching period. We will count the best 8 out of 10 scores, so if students miss up to two workshops due, for example due to illness, students will not need to give the lecturer medical certificates. For online workshops students need to have their camera turned on for the whole duration of the workshop. The exemptions can be requested from the lecturers.

Workshop Structure

A worksheet will be made available before your workshop. The questions in the worksheet will be similar to those given in the text books. You will be expected to have completed the worksheet before attending the workshop.

A discussion group has been set up for each workshop group. You may scan the solution to your group's question and post it on the discussion group for your workshop. Please do not post it on the general (whole class) discussion group.

At the start of each workshop, the class will divide into small groups so that each person presenting a solution can check their answer with their peers and demonstrator. The person presenting the solution should feel free to ask for as much help as they want. During the next 15 to 20 minutes, each presenter will discuss their solution with the whole class. All students should participate and ask questions. The remaining time will be left free for students to ask questions or get some feedback about the assignments etc.

Please remember that you do get marks towards your total grade for presenting solutions during workshop times. For the first workshop, anybody interested in presenting a solution should use the discussion board to let their demonstrator know.

The solutions to the worksheets will not be posted on Wattle, they are to be presented and discussed in the workshop. Do not send e-mails at the end of the semester asking for a copy of the solutions; attend regularly the workshops.

Value: 6 %
Learning Outcomes: 1,2,3,4,5

Assignments

There are 3 assignments due over the semester. One assignment will be for vector calculus part of the course and the other for the ODE part of the course.

When you use Matlab (or some other package) as part of the solution (including generating plots), you must submit your code with the assignment. This can either be printed and scanned with a hand written solution, or cut and pasted into a typeset solution.

It is intended that marked assignments be returned to students two weeks after the submission's deadline.

Assignment 1 available on Friday week 3. Due Tuesday March 23rd (week 5)

Assignment 2 available on Friday week 6. Due Tuesday April 27th (week 8)

Assignment 3 available on Friday week 9. Due Tuesday May 18th (week 11)

Value: 11 %
Learning Outcomes: 1,2,3,4,5

Online tests

There will be 4 online tests which will take place during the workshop a student is enrolled in. Students have to sit for their test at their workshop. If a test is taken outside of the designated workshop, the mark for the test will be zero.

If a test is missed a test due to unforeseen circumstances (e.g. illness) the student must provide supporting documentation to the lecturers to arrange a test at another time.

The tests will be Wattle quizzes. We will count the best 3 out of 4 score.

Wattle quiz 1 in week 4

Wattle quiz 2 in week 6

Wattle quiz 3 in week 9

Wattle quiz 4 in week 12

Value: 6 %
Due Date: 01/03/2021
Return of Assessment: 28/05/2021
Learning Outcomes: 1,2,3,4,5

Quizzes

There are 11 online WebAssign weekly quizzes due over the semester. We will count the best 9 out of 11 scores. Instructions on how to access WebAssign will become available on Wattle.

1. Online WebAssign quiz 1 due on Monday the 1st of March (week 2) by 11.59pm.
2. Online WebAssign quiz 2 due on Tuesday the 9th of March (week 3) by 11.59pm
3. Online WebAssign quiz 3 due on Monday the 15th of March (week 4) by 11.59pm.
4. Online WebAssign quiz 4 due on Monday the 22nd of March (week 5) by 11.59pm.
5. Online WebAssign quiz 5 due on Monday the 29th of March (week 6) by 11.59pm.
6. Online WebAssign quiz 6 due on Monday the 19th April (week 7) by 11.59pm.
7. Online WebAssign quiz 7 due on Monday the 26th of April (week 8) by 11.59pm.
8. Online WebAssign quiz 8 due on Monday the 3rd of May (week 9) by 11.59pm.
9. Online WebAssign quiz 9 due on Monday the 10th of May (week 10) by 11.59pm.
10. Online WebAssign quiz 10 due on Monday the 17th of May (week 11) by 11.59pm.
11. Online WebAssign quiz 11 due on Monday the 24th of May (week 12) by 11.59pm.

Value: 20 %
Due Date: 02/06/2020
Return of Assessment: 16/06/2020
Learning Outcomes: 1,2,3,4,5

Research project

Students will be given the project related to regular and chaotic dynamics. The topic will be announced early in the semester. A project report is due at the end of the semester and will be marked according to the student's attempt to complete the research project.

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

## Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

## Hardcopy Submission

No hard copy submissions will be accepted unless approved by the lecturer. Students should either type their assignments or scan/take a photograph of their hand-written assignments and submit them for marking via Wattle. They also must utilise the Assignment Cover Sheet. The quality of scans/photographs must be good. If the demonstrator cannot read parts of an assignment they will give zero marks to that part. Please keep a copy of tasks completed for your own records.

## Late Submission

Late submissions of assignments without an extension that is approved by the lecturer are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assignments will not be accepted after a date to be specified when the assignment is set.

## Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

## Returning Assignments

Assignments will be submitted and returned via Wattle.

## Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

## Resubmission of Assignments

No resubmission is permitted.

## Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

## Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

## Convener

 Prof Lilia Ferrario Lilia.Ferrario@anu.edu.au

### Research Interests

Theoretical Astrophysics. Research on compact stars (white dwarfs, neutron stars) and magnetically confined accretion flows. Galactic archaeology (formation of our Galaxy) using white dwarf stars.

### Prof Lilia Ferrario

 Wednesday 11:00 12:00 Thursday 13:00 14:00 Thursday 13:00 14:00

## Instructor

 Galina Levitina 6125290 Galina.Levitina@anu.edu.au

### Galina Levitina

 Tuesday 11:00 12:00

## Instructor

 Prof Lilia Ferrario 6125290 Lilia.Ferrario@anu.edu.au

### Prof Lilia Ferrario

 Wednesday 11:00 12:00 Thursday 13:00 14:00 Thursday 13:00 14:00

## Instructor

 Zhisong Qu 6125290 zhisong.qu@anu.edu.au